• Journal of the Korean Data and Information Science Society
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• 제24권4호
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• pp.911-918
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• 2013

This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

• 한국수학교육학회지시리즈A:수학교육
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• 제55권2호
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• pp.193-208
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• 2016

This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.

• Communications for Statistical Applications and Methods
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• 제15권5호
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• pp.655-666
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• 2008

Small sample likelihood based inference for the shape parameter of the inverse Gaussian distribution is the purpose of this paper. When shape parameter is of interest, the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are derived. Hsieh (1990) gave a statistical inference for the shape parameter based on an exact method. Throughout simulation, we will compare the statistical properties of the proposed statistics to the statistic given by Hsieh (1990) in term of confidence interval and power of test. We also discuss a real data example.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1173-1181
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• 2008

In this paper, when the parameter of interest is the shape parameter in Pareto distribution, we develop likelihood based inference for this parameter. Specially, we develop signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the shape parameter. It is well-known that as sample size grows, the modified signed log-likelihood ratio statistic converges to standard normal distribution faster than the signed log-likelihood ratio statistic. But the computation of the modified signed log-likelihood statistic is hard or even impossible when the sufficient statistics and the ancillary statistics are not clear. In this case, one can consider an approximation to the modified signed log-likelihood statistic. Specially, when the parameter of interest is informationally orthogonal to the nuisance parameters, we propose the approximate modified signed log-likelihood statistic. Through simulation, we investigate the performances of the proposed statistics with the signed log-likelihood statistic.

• 한국언어정보학회:학술대회논문집
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• 한국언어정보학회 2002년도 Language, Information, and Computation Proceedings of The 16th Pacific Asia Conference
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• pp.187-194
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• 2002

In this paper it has been proposed that concession should be analysed as involving scalar implicatures and that an alternative set of situations have to be assumed to account for the the relative nature of likelihood of event occurrence. This paper also claims that the notion of likelihood is the basis of the corresponding pragmatic inference and a universal quantification effect. Unexpectedness, which is conceptually tied to concession, on the other hand involves the same kind of pragmatic inference but presuppose the existence of an alternative set of individuals instead of an alternative set of situations.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.109-114
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• 2003

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter, which is peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose nonparametric maximum likelihood estimator of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of the Korean Statistical Society
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• 제33권3호
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• pp.303-312
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• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of the Korean Data and Information Science Society
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• 제14권2호
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• pp.413-428
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.457-470
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• 2003

The comparison of two or more Lorenz curves of Pareto distributions of first kind under arbitrary order restriction is studied. The problem is turned out to be a statistical inference problem concerning scale parameters under order restriction. We assume that the location parameters of Palate distributions are completely unknown. In this paper the maximum likelihood estimation and likelihood ratio tests for and against order restriction are proposed.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2007년도 한국컴퓨터종합학술대회논문집 Vol.34 No.1 (C)
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• pp.263-266
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• 2007

본 논문은 베이지안 통계 추론에 대하여 논의한다. 논문은 베이지안 추론, Markov Chain과 Monte Carlo 적분, MCMC(Markov Chain Monte Carlo) 기법, Metropolis-Hastings 알고리즘, Gibbs 샘플링, Maximum Likelihood Estimation, EM 알고리즘, 상실된 데이터 보완 기법, BMA(Bayesian Model Averaging) 순서로 논의를 진행한다. 이러한 통계적 기법들은 대용량의 데이터를 처리하는 생물학, 의학, 생명 공학, 과학과 공학, 그리고 일반 데이터 조사와 처리 등에 사용되고 있으며, 최적의 추론 결과를 이끌어 내는데 중요한 방법을 제공하고 있다. 그리고 마지막으로 PC(Principal Component) 분석 기법에 대하여 논의한다. PC 분석 기법도 데이터 분석과 연구에 많이 활용된다.